Homoclinic intersections for geodesic flows on convex spheres

Zhihong Xia, Pengfei Zhang

Research output: Chapter in Book/Report/Conference proceedingChapter


In this paper, we study some generic properties of the geodesic flows on a convex sphere. We prove that, Cr generically (2 ≤ r ≤ ∞), every hyperbolic closed geodesic on S2 admits some transverse homoclinic intersections.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages18
StatePublished - 2017

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


  • Closed geodesic
  • Convex spheres
  • Elliptic geodesic
  • Geodesic flow
  • Hyperbolic geodesic
  • Nonlinearly stable
  • Prime-end compactification
  • Transverse homoclinic intersections

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Homoclinic intersections for geodesic flows on convex spheres'. Together they form a unique fingerprint.

Cite this